The authors consider the design of a single-server queue with finite buffer capacity. Arrivals follow a Poisson distribution and service times have phase-type distributions. It is possible to switch the service rate between the normal and higher rates. A bi-level hysteretic control policy is considered where two trigger points, say u and l, are used for changes in service rate. When the number in the system exceeds u, the service rate is increased and it returns to the normal level only when the number in the system drops to l (0<l<u). Algorithms to compute the equilibrium probability vector are presented along with a detailed discussion of various issues arising in their implementation. Numerical results are presented along with discussions of the behavior of the system and of the effect of changes in the various model parameters. The paper concludes with a discussion on how the heuristic understanding of the system behavior gained can be exploited in performing an efficient numerical search for optimal parameter values. Details on extensions of the proposed algorithmic procedure to systems with more general arrival processes are also presented.
